Two bodies of masses 8 ~kg are placed at the vertices A and B of an equilateral triangle A B C . A third body of mass 2 ~kg is placed at the centroid G of the triangle. If A G=B G=C G=1 ~m , where should a fourth body of mass 4 ~kg be place

Question

Two bodies of masses 8 ~kg are placed at the vertices A and B of an equilateral triangle A B C . A third body of mass 2 ~kg is placed at the centroid G of the triangle. If A G=B G=C G=1 ~m , where should a fourth body of mass 4 ~kg be placed, so that the resultant force on the 2 ~kg body is zero?

Quantrex Academy · Accepted Answer

Correct answer: B. At a point P on the line C G such that P G= 1 2 ~m

According to the question, the arrangement of the masses is as shown below, Gravitational force between two masses is given as F= G m₁ m₂ r² where, G= gravitational constant and r= distance between them. From the given values, we can say that force between masses at A and G . = Force between masses at B and G . array ll & F_ A = G m_ A m_ G A G² and F_ B = G m_ B m_ G B G² or & F_ A =F_ B = G 8 2 1² =16 G...(i) array [ . Given, m₁=m_ A =m_ B =8 ~kg , m₂=m_ G =2 ~kg , A G=B G=r=1 ~m ] From the figure, resultant of F

Two bodies of masses 8 ~kg are placed at the vertices A and B of an equilateral triangle A B C . A third body of mass 2 ~kg is placed at the centroid G of the triangle. If A G=B G=C G=1 ~m , where should a fourth body of mass 4 ~kg be placed, so that the resultant force on the 2 ~kg body is zero?

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